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Instance sporttournament20
This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 192.00000110 (ANTIGONE) 192.00000020 (BARON) 216.00000000 (COUENNE) 214.14523640 (CPLEX) 192.00000000 (GUROBI) 192.00000000 (LINDO) 192.00000000 (SCIP) 192.00000000 (SHOT) |
| Referencesⓘ | Elf, Matthias, Jünger, Michael, and Rinaldi, Giovanni, Minimizing Breaks by Maximizing Cuts, Operations Research Letters, 31:5, 2003, 343-349. |
| Sourceⓘ | POLIP instance maxcut/sched-20-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 191 |
| #Binary Variablesⓘ | 190 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 190 |
| #Nonlinear Binary Variablesⓘ | 190 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 1 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 191 |
| #Nonlinear Nonzeros in Jacobianⓘ | 190 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 720 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 190 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 190 |
| Average blocksize in Hessian of Lagrangianⓘ | 190.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 4.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1 0 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 191 1 190 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 191 1 190 0
*
* Solve m using MINLP maximizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181
,b182,b183,b184,b185,b186,b187,b188,b189,b190,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101
,b102,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114
,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127
,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153
,b154,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166
,b167,b168,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179
,b180,b181,b182,b183,b184,b185,b186,b187,b188,b189,b190;
Equations e1;
e1.. 2*b1*b5 - 2*b1 - 2*b5 + 2*b1*b8 - 2*b8 + 2*b1*b23 - 4*b23 - 2*b1*b35 + 4*
b35 + 2*b2*b3 - 2*b2 - 2*b3 + 2*b2*b33 - 4*b33 - 2*b2*b144 + 2*b2*b150 + 2
*b3*b84 - 2*b84 - 2*b3*b106 + 2*b106 + 2*b3*b140 + 2*b4*b86 - 2*b4 - 2*b86
+ 2*b4*b107 - 2*b107 + 2*b4*b140 - 2*b4*b158 + 2*b5*b6 - 2*b6 + 2*b5*b136
- 2*b5*b151 + 2*b6*b52 - 4*b52 + 2*b6*b72 - 4*b72 - 2*b6*b161 + 2*b7*b17
- 2*b7 - 2*b17 + 2*b7*b103 - 4*b103 + 2*b8*b141 - 2*b8*b146 + 2*b8*b162
+ 2*b9*b27 - 2*b9 - 4*b27 - 2*b9*b39 - 2*b39 + 2*b9*b72 + 2*b9*b163 + 2*
b10*b49 - 2*b10 - 2*b49 + 2*b10*b65 - 2*b65 + 2*b10*b68 - 2*b68 - 2*b10*
b133 + 2*b11*b47 - 2*b11 - 4*b47 + 2*b11*b157 + 2*b12*b32 - 4*b12 - 2*b32
+ 2*b12*b49 + 2*b12*b133 + 2*b12*b165 + 2*b13*b14 - 2*b13 - 4*b14 - 2*b13
*b34 + 2*b34 + 2*b13*b136 + 2*b13*b144 + 2*b14*b89 - 2*b89 + 2*b14*b113 -
2*b113 + 2*b14*b135 + 2*b15*b26 - 2*b15 - 2*b26 + 2*b15*b38 - 2*b38 + 2*
b15*b146 - 2*b15*b175 - 2*b16*b17 - 2*b16 + 2*b16*b45 - 2*b45 + 2*b16*b62
- 4*b62 + 2*b16*b169 + 2*b17*b18 - 2*b18 + 2*b17*b61 - 4*b61 + 2*b18*b62
+ 2*b19*b20 - 2*b19 - 2*b20 + 2*b19*b21 - 2*b21 + 2*b19*b67 - 4*b67 - 2*
b19*b150 + 2*b20*b23 + 2*b20*b49 - 2*b20*b111 + 2*b111 + 2*b21*b23 + 2*b21
*b89 - 2*b21*b180 - 2*b22*b24 + 2*b22 - 2*b24 - 2*b22*b110 + 4*b110 - 2*
b22*b136 + 2*b22*b139 + 2*b23*b24 + 2*b24*b113 + 2*b24*b166 + 2*b25*b41 -
2*b25 - 2*b41 + 2*b25*b146 + 2*b25*b151 - 2*b25*b167 + 2*b26*b55 - 4*b55
- 2*b26*b73 - 2*b73 + 2*b26*b75 - 4*b75 + 2*b27*b56 - 4*b56 + 2*b27*b154
+ 2*b27*b167 + 2*b28*b29 - 2*b28 - 2*b29 - 2*b28*b44 + 2*b44 + 2*b28*b98
- 2*b98 + 2*b28*b171 + 2*b29*b59 - 2*b59 + 2*b29*b80 - 2*b80 - 2*b29*b157
+ 2*b30*b31 - 2*b30 - 2*b31 + 2*b30*b124 - 2*b124 - 2*b30*b171 + 2*b30*
b172 + 2*b31*b80 + 2*b32*b33 - 2*b32*b34 + 2*b32*b108 - 2*b108 + 2*b33*b36
- 4*b36 + 2*b33*b89 + 2*b34*b36 - 2*b34*b87 - 2*b87 - 2*b35*b37 - 2*b37
- 2*b35*b88 + 2*b88 - 2*b35*b139 + 2*b36*b37 + 2*b36*b141 + 2*b37*b161 +
2*b37*b166 + 2*b38*b40 - 2*b40 + 2*b38*b135 - 2*b38*b145 + 2*b39*b54 - 4*
b54 + 2*b39*b151 + 2*b39*b153 + 2*b40*b54 + 2*b40*b115 - 2*b115 - 2*b40*
b183 - 2*b41*b53 - 2*b53 + 2*b41*b75 + 2*b41*b94 - 4*b94 + 2*b42*b152 - 4*
b42 + 2*b42*b164 + 2*b42*b167 + 2*b42*b175 - 2*b43*b44 - 2*b43 + 2*b43*
b130 + 2*b43*b131 + 2*b43*b164 + 2*b44*b79 - 2*b79 - 2*b44*b184 + 2*b45*
b46 - 4*b46 + 2*b45*b121 - 2*b121 - 2*b45*b178 + 2*b46*b79 + 2*b46*b102 -
2*b102 + 2*b46*b157 + 2*b47*b48 - 2*b48 + 2*b47*b101 - 4*b101 + 2*b47*b171
+ 2*b48*b102 - 2*b49*b110 - 2*b50*b141 + 4*b50 - 2*b50*b144 - 2*b50*b160
- 2*b50*b182 - 2*b51*b153 - 2*b51 + 2*b51*b182 + 2*b51*b183 + 2*b51*b186
+ 2*b52*b74 - 4*b74 + 2*b52*b115 + 2*b52*b153 + 2*b53*b71 - 2*b71 + 2*b53
*b74 + 2*b53*b183 + 2*b54*b94 + 2*b54*b116 - 4*b116 + 2*b55*b57 - 4*b57 +
2*b55*b156 + 2*b55*b175 + 2*b56*b58 - 4*b58 + 2*b56*b117 - 4*b117 + 2*b56*
b149 + 2*b57*b58 + 2*b57*b116 + 2*b57*b148 + 2*b58*b129 + 2*b58*b170 + 2*
b59*b61 - 2*b59*b130 + 2*b59*b178 - 2*b60*b80 + 2*b60 - 2*b60*b100 - 2*
b100 + 2*b60*b126 - 4*b126 - 2*b60*b128 + 2*b61*b99 - 2*b99 + 2*b61*b126
+ 2*b62*b63 - 2*b63 + 2*b62*b125 - 4*b125 + 2*b63*b126 - 2*b64*b66 + 2*
b64 - 2*b66 - 2*b64*b133 + 2*b65*b67 + 2*b65*b173 - 2*b65*b174 + 2*b66*b67
+ 2*b66*b150 + 2*b66*b174 + 2*b67*b69 - 2*b69 - 2*b68*b88 + 2*b68*b144 +
2*b68*b159 + 2*b69*b85 - 2*b85 + 2*b69*b88 - 2*b69*b110 + 2*b70*b71 - 2*
b70 + 2*b70*b90 - 2*b90 - 2*b70*b151 + 2*b70*b186 + 2*b71*b73 - 2*b71*b166
+ 2*b72*b93 - 4*b93 + 2*b72*b162 + 2*b73*b92 - 2*b92 + 2*b73*b93 + 2*b74*
b76 - 2*b76 + 2*b74*b116 + 2*b75*b77 - 4*b77 + 2*b75*b154 + 2*b76*b77 + 2*
b76*b93 - 2*b76*b131 + 2*b77*b119 + 2*b119 + 2*b77*b184 + 2*b78*b122 - 2*
b78 - 2*b122 - 2*b78*b143 + 2*b78*b169 + 2*b78*b184 + 2*b79*b124 - 2*b79*
b147 + 2*b80*b188 - 2*b81*b84 + 2*b81 - 2*b81*b137 + 2*b82*b84 - 2*b82 + 2
*b82*b165 - 2*b83*b85 + 2*b83 - 2*b83*b134 - 2*b83*b150 + 2*b83*b177 + 2*
b84*b85 + 2*b85*b87 + 2*b86*b139 + 2*b86*b159 - 2*b86*b160 + 2*b87*b109 -
2*b109 + 2*b87*b160 - 2*b88*b187 - 2*b89*b90 + 2*b90*b91 - 2*b91 + 2*b90*
b187 + 2*b91*b92 + 2*b91*b112 - 4*b112 - 2*b91*b146 - 2*b92*b113 + 2*b92*
b176 + 2*b93*b95 - 2*b95 + 2*b94*b96 - 4*b96 + 2*b94*b152 + 2*b95*b96 + 2*
b95*b131 - 2*b95*b190 + 2*b96*b97 + 2*b97 + 2*b96*b181 - 2*b97*b98 - 2*b97
*b129 - 2*b97*b156 + 2*b98*b100 + 2*b98*b181 + 2*b99*b101 - 2*b99*b142 + 2
*b99*b170 + 2*b100*b101 + 2*b100*b142 + 2*b101*b103 + 2*b102*b104 - 2*b104
- 2*b102*b132 + 2*b103*b104 + 2*b103*b132 + 2*b105*b107 - 2*b105 + 2*b105
*b158 - 2*b106*b109 - 2*b106*b138 + 2*b106*b179 + 2*b107*b109 - 2*b107*
b173 + 2*b108*b137 + 2*b108*b158 - 2*b108*b180 + 2*b109*b180 - 2*b110*b185
+ 2*b111*b112 - 2*b111*b155 - 2*b111*b186 + 2*b112*b145 + 2*b112*b185 + 2
*b113*b114 - 4*b114 + 2*b114*b145 + 2*b114*b168 + 2*b114*b176 + 2*b115*
b117 - 2*b115*b163 + 2*b116*b118 - 4*b118 + 2*b117*b118 + 2*b117*b190 + 2*
b118*b120 - 2*b120 + 2*b118*b143 - 2*b119*b121 - 2*b119*b142 - 2*b119*b154
+ 2*b120*b121 - 2*b120*b156 + 2*b120*b178 + 2*b121*b123 - 2*b123 + 2*b122
*b124 + 2*b122*b125 - 2*b122*b129 + 2*b123*b125 - 2*b123*b132 + 2*b123*
b147 - 2*b124*b189 + 2*b125*b189 + 2*b126*b127 - 2*b127 + 2*b127*b189 + 2*
b128*b129 - 2*b128*b130 + 2*b128*b132 + 2*b130*b148 - 2*b131*b149 + 2*b133
*b134 - 2*b135*b136 - 2*b135*b153 + 2*b137*b138 - 2*b137*b159 - 2*b139*
b140 - 2*b140*b155 - 2*b141*b145 + 2*b142*b143 - 2*b143*b164 - 2*b147*b148
+ 2*b147*b149 - 2*b148*b152 - 2*b149*b170 - 2*b152*b184 - 2*b154*b181 + 2
*b155*b180 + 2*b155*b185 + 2*b156*b163 - 2*b157*b172 - 2*b158*b179 - 2*
b159*b165 + 2*b160*b187 + 2*b161*b182 - 2*b161*b183 - 2*b162*b166 - 2*b162
*b168 - 2*b163*b164 - 2*b165*b177 - 2*b167*b168 + 2*b168*b190 - 2*b169*
b170 - 2*b169*b171 - 2*b175*b176 - 2*b176*b190 - 2*b178*b181 - 2*b182*b185
- 2*b186*b187 - 2*b188*b189 + objvar =L= 0;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc